In the later rounds of the NFL draft, it’s difficult to find players who are going to contribute at any level. However, since Bill Belichick’s first draft as head coach in 2000, the Patriots have been one of the best teams in the league finding these “diamond in a rough” type players.

Tom Brady – Round 6 (2000)

David Givens – Round 7 (2002)

Dan Koppen – Round 5 (2003)

Tully Banta-Cain – Round 7 (2003)

Matt Cassel – Round 7 (2005)

But, Belichick and the scouting team came up dry in 2006.

Jeremy Mincey

Round: 6

Pick: 191

College: Florida

Position: Outside LB

Belichick has never been shy about drafting Florida players because of his connection with UF coach Urban Meyer. Since Meyer joined Florida, Belichick has drafted five of his players, including three from the 2010 NFL Draft. Defensive end Jeremy Mincy was the second UF player to be taken in the 2006 draft and like the first one, Chad Jackson, he didn’t amount to much.

Mincey only played two years at Florida, but during that time he earned second-team all SEC honors as a senior. At 6’3” 260, the Patriots tried to convert the DE to OLB at the pro-level as Mincey posted a 40-yard-dash time of 4.79.

Unfortunately for Mincy, he didn’t make it through training camp and was released in the summer of 2006 before signing with the San Francisco 49ers.

OLBs taken after Mincey (that have made an impact)

N/A

Dan Stevenson

Round: 6

Pick: 205

College:Notre Dame

Position: Offensive Guard

Like the previous selection of Mincy, it can be assumed that Belichick’s coaching connections led him to the drafting of Dan Stevenson.

Stevenson had a solid career at Notre Dame, where he was a three-year starter and considered the best of the Fighting Irish offensive lineman.

Despite having one of the best offensive line coaches in the NFL in Dante Scarnecchia, the Patriots couldn’t transfer Stevenson’s medial success to the NFL. Stevenson spent the first half of his rookie season on New England’s practice squad before being released in November 2007.

OGs taken after Stevenson (that have made an impact)

N/A

Le Kevin Smith

Round: 6

Pick: 206

College: Nebraska

Position: Defensive Tackle

Le Kevin Smith proved to be a serviceable defensive lineman while in New England. In 2007, Smith appeared in 13 games and had 14 tackles.

The 6’3” 306-pound DT only improved from his decent 2007 season, notching 21 tackles in 2008.

After the Patriots traded Richard Seymour to the Oakland Raiders, some thought Smith could help fill in and succeed. However, the Patriots thought differently.

In August 2009, the Patriots traded Smith to the Denver Broncos in exchange for 2010 fifth round draft pick, which turned into the drafting of Taylor Price after a few other transactions.

DTs taken after Smith (that have made an impact)

N/A

Willie Andrews

Round: 7

Pick: 229

College: Baylor

Position: Kickoff Specialist/Defensive Back

The special teams ace had a solid rookie season for the Patriots, including a 74-yard kick return touchdown against the Miami Dolphins.

However, the defensive back’s troubled past eventually led to his release.

In February 2008, Massachusetts police found half-a-pound of marijuana on Andrews and $6,800 of cash. That same year, in June, Andrews was charged with assault with a dangerous weapon.

Belichick and co. wasted little time after that, releasing Andrews.

After his tenure with New England, Andrews was signed by the Florida Tuskers in the UFL.

Although the consensus agreed that Andrews would never be a starter in the NFL, it was clear that he could have been a solid special teams player for years to come. Unfortunately multiple run-ins with the law later and Andrews ran himself out of the NFL.

DBs taken after Andrews (that have made an impact)

Matthew Marcantonio is the Patriots and college football editor at Sports of Boston. Marcantonio has contributed for two newspapers; the Sentinel & Enterprise (Leominster, Mass) and The Advocate (Baton Rouge, La) and held internships with The Bleacher Report and Sports Illustrated.